| Course title | Introduction to Differential Equations |
|---|---|
| Course code | UMB/587 |
| Organizational form of instruction | Lecture + Lesson |
| Level of course | Bachelor |
| Year of study | not specified |
| Frequency of the course | In each academic year, in the summer semester. |
| Semester | Summer |
| Number of ECTS credits | 6 |
| Language of instruction | Czech |
| Status of course | Compulsory, Compulsory-optional |
| Form of instruction | Face-to-face |
| Work placements | This is not an internship |
| Recommended optional programme components | None |
| Lecturer(s) |
|---|
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| Course content |
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Content of lectures: 1. Differential equations as description of dynamical processes in science. 2. Existence of a solution for the Cauchy problem 3. Piccard-Lindelof method of approximate solutions 4. Elementary methods of solution, separation of variables 5. Linear differential equations of the n-th order, fundamental system of solutions, method of variation of constants 6. Linear differential equations of the n-th order with constant coefficients. 7. Systems of linear differential equations. Fundamental set of solutions as a linear vector space. 8. Systems of linear differential equations with constant parameters 9. Stability of zero solution for linear systems of differential equations 10. Non-linear systems of differential equations. Local stability of equilibria. 11. Analysis of Lotka-Volterra equations 12. Lyapunov stability 13. Limit cycles, Poincaré-Bendixon theory Content of practicals: Solving differential equations.
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| Learning activities and teaching methods |
Monologic (reading, lecture, briefing), Work with text (with textbook, with book)
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| Learning outcomes |
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To develop basic concepts of ordinary differential equations.
Students can build, analyse and solve Cauchy problems for ordinary differential equations. |
| Prerequisites |
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Single variable differential and integral calculus, linear algebra.
UMB/565 and UMB/CV551 ----- or ----- UMB/551 |
| Assessment methods and criteria |
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Combined exam
1. Attendance at least 80% 2. Students must obtain at least 50% points from tests during the course |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Science | Study plan (Version): Applied Informatics (1) | Category: Informatics courses | - | Recommended year of study:-, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Mathematics for future teachers (1) | Category: Mathematics courses | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Physics (1) | Category: Physics courses | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Mathematics for future teachers (1) | Category: Mathematics courses | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Biophysics (1) | Category: Physics courses | 2 | Recommended year of study:2, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Applied Mathematics (2010) | Category: Mathematics courses | 2 | Recommended year of study:2, Recommended semester: Summer |